Solve ∣ 2 x − 3 ∣

To solve the equation $|2x - 3| = 1$, we need to consider the two possible cases for an absolute value equation.

Case 1: $2x - 3 = 1$

1. Solve for $x$: $2x - 3 = 1$ Add 3 to both sides: $2x = 4$ Divide by 2: $x = 2$

Case 2: $2x - 3 = -1$

1. Solve for $x$: $2x - 3 = -1$ Add 3 to both sides: $2x = 2$ Divide by 2: $x = 1$

Final Solution:

The solutions are $x = 2$ and $x = 1$.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How do you solve an absolute value inequality?
2. What are the properties of absolute value functions?
3. How would the solution change if the equation was $|2x - 3| = 5$?
4. Can absolute value equations have no solutions?
5. How do you graph an absolute value equation?

Tip: When solving absolute value equations, always consider both the positive and negative cases!